Abstract
We give a necessary and sufficient condition for the distribution function of $n^{-1/2} \sum^n_{i=1} X_i$, where the $X_i$ are independently identically distributed with $EX_1 = 0, EX^2_1 = 1$ and $E|X_1|^{k+3} < \infty$, to possess an Edgeworth expansion to $k$ terms. The condition is not practicable but clarifies the relation between the existence of an Edgeworth expansion and the smoothness of the distribution function of the sum.
Citation
P. J. Bickel. J. Robinson. "Edgeworth Expansions and Smoothness." Ann. Probab. 10 (2) 500 - 503, May, 1982. https://doi.org/10.1214/aop/1176993873
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